2,478 research outputs found
Saturation numbers in tripartite graphs
Given graphs and , a subgraph is an -saturated
subgraph of if , but for all . The saturation number of in , denoted
, is the minimum number of edges in an -saturated subgraph
of . In this paper we study saturation numbers of tripartite graphs in
tripartite graphs. For and , , and sufficiently
large, we determine and
exactly and
within an additive constant.
We also include general constructions of -saturated subgraphs of
with few edges for .Comment: 18 pages, 6 figure
Minimum saturated subgraphs of tripartite graphs
Let F and H be graphs. A subgraph G of H is an F-saturated subgraph of H if F is not a subgraph of G and F is a subgraph of G+e for any edge e in E(H) E(G). The saturation number of F in H is the minimum number of edges in a F-saturated subgraph of H. We denote the saturation number of F in H as sat(H,F). In this thesis we review the history of saturated subgraphs, and prove new results on saturated subgraphs of tripartite graphs. Let Ka,b,c be a compete tripartite graph, with partite sets of size a, b, and c. Specifically, we determine sat(Kn1,n2,n3,Kl,l,l), for n1≥ n2≥ n3, when n2 bounded by a linear function of n3. We also examine the special case when l=1 and determine sat(Kn1,n2,n3,K3)$ for n1≥ n2≥ n3, and n_3 sufficiently large. We also consider two natural variants of saturated subgraphs that arise in the tripartite setting. We examine the behavior of these extensions using illustrative examples to highlight the differences between these variations and the original problem
Identifying Overlapping and Hierarchical Thematic Structures in Networks of Scholarly Papers: A Comparison of Three Approaches
We implemented three recently proposed approaches to the identification of
overlapping and hierarchical substructures in graphs and applied the
corresponding algorithms to a network of 492 information-science papers coupled
via their cited sources. The thematic substructures obtained and overlaps
produced by the three hierarchical cluster algorithms were compared to a
content-based categorisation, which we based on the interpretation of titles
and keywords. We defined sets of papers dealing with three topics located on
different levels of aggregation: h-index, webometrics, and bibliometrics. We
identified these topics with branches in the dendrograms produced by the three
cluster algorithms and compared the overlapping topics they detected with one
another and with the three pre-defined paper sets. We discuss the advantages
and drawbacks of applying the three approaches to paper networks in research
fields.Comment: 18 pages, 9 figure
Electroencephalographic field influence on calcium momentum waves
Macroscopic EEG fields can be an explicit top-down neocortical mechanism that
directly drives bottom-up processes that describe memory, attention, and other
neuronal processes. The top-down mechanism considered are macrocolumnar EEG
firings in neocortex, as described by a statistical mechanics of neocortical
interactions (SMNI), developed as a magnetic vector potential . The
bottom-up process considered are waves prominent in synaptic
and extracellular processes that are considered to greatly influence neuronal
firings. Here, the complimentary effects are considered, i.e., the influence of
on momentum, . The canonical
momentum of a charged particle in an electromagnetic field, (SI units), is calculated, where the charge of
is , is the magnitude of the charge of an
electron. Calculations demonstrate that macroscopic EEG can be
quite influential on the momentum of ions, in
both classical and quantum mechanics. Molecular scales of
wave dynamics are coupled with fields developed at macroscopic
regional scales measured by coherent neuronal firing activity measured by scalp
EEG. The project has three main aspects: fitting models to EEG
data as reported here, building tripartite models to develop
models, and studying long coherence times of waves in the
presence of due to coherent neuronal firings measured by scalp
EEG. The SMNI model supports a mechanism wherein the interaction at tripartite synapses, via a dynamic centering
mechanism (DCM) to control background synaptic activity, acts to maintain
short-term memory (STM) during states of selective attention.Comment: Final draft. http://ingber.com/smni14_eeg_ca.pdf may be updated more
frequentl
On the universal structure of human lexical semantics
How universal is human conceptual structure? The way concepts are organized
in the human brain may reflect distinct features of cultural, historical, and
environmental background in addition to properties universal to human
cognition. Semantics, or meaning expressed through language, provides direct
access to the underlying conceptual structure, but meaning is notoriously
difficult to measure, let alone parameterize. Here we provide an empirical
measure of semantic proximity between concepts using cross-linguistic
dictionaries. Across languages carefully selected from a phylogenetically and
geographically stratified sample of genera, translations of words reveal cases
where a particular language uses a single polysemous word to express concepts
represented by distinct words in another. We use the frequency of polysemies
linking two concepts as a measure of their semantic proximity, and represent
the pattern of such linkages by a weighted network. This network is highly
uneven and fragmented: certain concepts are far more prone to polysemy than
others, and there emerge naturally interpretable clusters loosely connected to
each other. Statistical analysis shows such structural properties are
consistent across different language groups, largely independent of geography,
environment, and literacy. It is therefore possible to conclude the conceptual
structure connecting basic vocabulary studied is primarily due to universal
features of human cognition and language use.Comment: Press embargo in place until publicatio
Exploring the Local Orthogonality Principle
Nonlocality is arguably one of the most fundamental and counterintuitive
aspects of quantum theory. Nonlocal correlations could, however, be even more
nonlocal than quantum theory allows, while still complying with basic physical
principles such as no-signaling. So why is quantum mechanics not as nonlocal as
it could be? Are there other physical or information-theoretic principles which
prohibit this? So far, the proposed answers to this question have been only
partially successful, partly because they are lacking genuinely multipartite
formulations. In Nat. Comm. 4, 2263 (2013) we introduced the principle of Local
Orthogonality (LO), an intrinsically multipartite principle which is satisfied
by quantum mechanics but is violated by non-physical correlations.
Here we further explore the LO principle, presenting new results and
explaining some of its subtleties. In particular, we show that the set of
no-signaling boxes satisfying LO is closed under wirings, present a
classification of all LO inequalities in certain scenarios, show that all
extremal tripartite boxes with two binary measurements per party violate LO,
and explain the connection between LO inequalities and unextendible product
bases.Comment: Typos corrected; data files uploade
- …